Question

Find the image of •DEF under the translation of (x, y) --> (x + 7, y + 2)•GHJ •NPQ•KLM•ABC

Answer 1

By definition, a Translation is a transformation in which the figure is moved without changing its size or shape.

In transformations, the original figure is called "Pre-Image" and the figure after the transformation is called "Image".

You can identify that, in this case, the Pre-Image is DEF. Notice that the coordinates of its vertices are:

$\begin{gathered} D(-5,1) \\ E(-2,4) \\ F(-2,1) \end{gathered}$

Since the rule for the translation is:

$(x,y)\rightarrow(x+7,y+2)$

You can apply it in oder to get the coordinates of its Image:

$\begin{gathered} D(-5,1)\rightarrow(-5+7,1+2)\rightarrow(2,3) \\ E(-2,4)\rightarrow(-2+7,4+2)\rightarrow(5,6) \\ F(-2,1)\rightarrow(-2+7,1+2)\rightarrow(5,3) \end{gathered}$

Analazing the figures given in the exercise, you can identify that:

$\begin{gathered} G(2,3) \\ H(5,6) \\ J(5,3) \end{gathered}$

Therefore, the figure GHJ is the Image of DEF.

The answer is: First option.